Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. Try lots of examples. What happens? Can you explain it?
When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
Can you work out how many of each kind of pencil this student
The following very clear explanation of the
solution to this problem came from Oliver of West Flegg Middle
School, Great Yarmouth:
Oliver then wrote out the sixteen times table
from 1 x 16 = 16 up to 32 x 16 = 48888 showing that the 512th
number is 48888.
If you do the same, you can also see that the
first 64 numbers start with 22 (running through all the
possibilities for the last 3 digits) the 64th number being 22888.
The next 64 numbers start with 24, the next 64 with 26, then 28,
42, 44, 46, 48, and so on. An alternative way to look at the
problem is to see the 512th number as the last number in the eighth
block of 64 numbers, (the block starting with 48), and so it is
Another good solution came from Luke of Flegg
High School, Great Yarmouth:
Ben of The Simon Langton Grammar School for
Boys in Canterbury also sent in a good solution to this one.